Fatou and Julia like sets II

TL;DR

This paper extends the study of Fatou and Julia like sets by introducing and analyzing escaping like sets and their properties for families of holomorphic functions, including connectedness results.

Contribution

It introduces escaping like sets and generalized escaping like sets for holomorphic functions, providing new insights into their properties and connectedness.

Findings

Defined escaping like sets and generalized escaping like sets

Proved connectedness of Julia like sets

Established distinctive properties of these sets

Abstract

This paper is a continuation of authors work: Fatou and Julia like sets,Ukranian J. Math., to appear/arXiv:2006.08308[math.CV](see [4]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic functions on an arbitrary domain, and establish some distinctive properties of these sets. The connectedness of the Julia like set is also proved.